What is $0\cdot 1+\frac{0}{1}+0^1+1^0$?
Anything multiplied by $0$, divided into $0$, or raised to a power with $0$ as the base will equal $0$. However, any nonzero number raised to the zero power equals $1$, so the first three terms equal zero while the last term equals $1$, for a total sum of $\boxed{1}$.